6x(x-8)=24

Solution for 6x(x-8)=24 equation:

6x(x-8)=24

We move all terms to the left:

6x(x-8)-(24)=0

We multiply parentheses

6x^2-48x-24=0

a = 6; b = -48; c = -24;
Δ = b2-4ac
Δ = -482-4·6·(-24)
Δ = 2880
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-24\sqrt{5}}{2*6}=\frac{48-24\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+24\sqrt{5}}{2*6}=\frac{48+24\sqrt{5}}{12}
$